Mathematical Emphasis
Investigation 1—Number Patterns in Changing Shapes

• Building designs that change in a regular way
• Building designs that grow according to number patterns
• Predicting later steps of number patterns and designs
• Making tables and graphs to display number patterns
• Investigating changes in the number of new tiles and the total number of tiles
• Using the language of speed and motion to describe number patterns

Investigation 2—Motion Stories, Graphs, and Tables

• Exploring relationships among distance, time, and speed
• Exploring irregular increases and decreases in speed
• Exploring ways that speed, time, and distance can be represented with tables, graphs, stories, and informal representations
• Interpreting intervals in a table and reflecting speed
• Interpreting steepness in a distance vs. time graph as reflecting speed

Supplemental Algebra Work

• Balancing algebraic expressions
• Translating number relations into algebraic equations
• Solving algebraic equations

Tips For Helping At Home
Questions To Ask:

• What do you need to find out?
• What did you do in class to get started?
• Have you solved similar problems that would help?
• Can you make a drawing (model) to explain your thinking?
• What would happen if…?
• What do you need to do next?
• How do you know your answer is reasonable?
• Has the question been answered?
• Are there any questions you want to ask your teacher?

Helping At Home

• Look at your child’s drawing of tile patterns and at the tables and graphs that that go with them. Ask your child to explain the patterns to you. How can you tell how the design will continue to grow? With your child, design some other tile patterns that grow in predictable ways.
• See if you can interpret the diagram your child makes to show how the speed changes during a walk along a straight line. Can you tell the story of the trip? It might be something like: “Start out walking slowly. Stop halfway for 6 seconds then run to the end.”
• Over the next few weeks, help your child look for things that change in different ways and at different speeds. Can you find some things that change faster and faster? Can you find things that change steadily? Can you find anything that changes by gradually slowing down? By gradually shrinking?
• Look in newspapers and other print materials for graphs and tables that show something changing over time. Work with your child to make sense of them.

Vocabulary Terms

Growth Patterns

Patterns that increase

Interval

The distance between two points

Line Graph

Line drawing which connects points showing the relationship between two variables like time and distance

Rate of Change

Increase or decrease in the value comparing the two variables

Table

Mathematical information organized into columns and rows

Mathematics Vocabulary Web site

Mathematics Strategy—Finding Patterns

Patterns in this unit are all examples of the fusion between geometry and numbers. As students experiment, they will see patterns from many different perspectives. Some of the patterns will lead children to understand general rules, like using step size to find a total at the nth step.

In an activity called “Twos Towers” children discover that the number of tiles is always double the step. This leads children to develop the simple rule that (Tiles) = 2 x (Step number). In an activity called “Squares” children discover that the number of tiles is always the square of the step number. They can come up with the rule that (Tiles) = (Step) x (Step). Both of these patterns and activities help children begin to understand simple algebraic equations and relationships.

Source: Investigations in Number, Data, and Space: Patterns of Change. Dale Seymour, 1998. (Pages 22 and 23)

Mathematics Game—Digits Down

Materials

Numeral Cards (No Wild Cards)

Record Sheet

Players: 2 or 3

Playing the Game

1. Players choose a target number (example: 1000).



2. Numeral cards are dealt out to all players. Number of cards dealt should be one more than the digits in the target number (example: 5 cards for any number in the thousands).



3. Players use any number of their numeral cards to make a number as close to the target as possible.



4. The target number and created numbers are written on players’ record sheets and the differences between the two are recorded. The differences are the players’ scores for the round.



5. Numeral cards are collected and reshuffled for each round.



6. After 3 rounds, the player with the lowest score wins. This player was able to create numbers closest to the target number.

Get to Numeral Cards (for printing)

Get to Record Sheet (for printing)